"If each barge operator leased 1 trip a day could they move the essantials at the same cost?"

no, not even close.

Runway is long enough for a fully loaded C130 to land but not strong enough.

Construction materials probably make up 95% of the weight and 80% of the volume of island cargo so adding a C130 would not solve the present barge siting problem. It would, rather, create rather obvious problems itself.